{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantum Fourier Transform  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classical discrete Fourier transform (DFT)   \n",
    "Given a vector $(x_0,\\ldots,x_{N-1})\\in\\mathbb{C}^N$, the discrete Fourier transform computes the vector $(y_0,\\ldots,y_{N-1})$ for which\n",
    "$$ y_j = \\frac{1}{\\sqrt{N}}\\sum_{k=0}^{N-1} x_k e^{\\frac{2\\pi i}{N}jk}.$$\n",
    "\n",
    "## Quantum Fourier Transformation (QFT)  \n",
    "In close analogy to the classical Fourier transform, the QFT takes an arbitrary input state $\\left|\\mathrm{input}\\right> = \\sum x_{j}\\left|j\\right>$ (with the orthonormal basis states $\\left|0\\right>$, $\\left|1\\right>$, ..., $\\left|N-1\\right>$), and maps it to the output state\n",
    "$$\\left|\\mathrm{output}\\right> = \\sum_{k} y_{k}\\left|k\\right>,$$ \n",
    "with coefficients\n",
    "$$y_{k}=\\frac{1}{\\sqrt{N}}\\sum_{n}x_{n}e^{2\\pi i\\cdot n\\cdot k/N}.$$\n",
    "\n",
    "## Quantum binary representation  \n",
    "We take $N=2^{n}$, with $n$ being the number of qubits. In the binary representation, the states $\\{\\left|x\\right>\\}$ read explicitly \n",
    "\n",
    "$$\\left|x\\right> = \\left|x_{1}x_{2}\\dots x_{n}\\right>,$$ \n",
    "where\n",
    "$$x = x_{1}2^{n-1}+x_{2}2^{n-2}+\\dots+x_{n}2^{0}.$$\n",
    "\n",
    "For example, in a four-qubit system $\\left|7\\right> = \\left|0111\\right>$ and $\\left|8\\right> = \\left|1000\\right>$.\n",
    "Similarly, we use the following notation to represent binary fractions:\n",
    "\n",
    "$$[0.x_{l}x_{l+1}\\dots x_{m}] = \\frac{x_{l}}{2^{1}} + \\frac{x_{l+1}}{2^{2}} + \\frac{x_{m}}{2^{m-l+1}}.$$\n",
    "\n",
    "## Product representation of QFT  \n",
    "The product representation of the QFT is important. Accordingly, the QFT can be expressed (up to normalization) as\n",
    "$$\\left|x_{1}x_{2}\\dots x_{n}\\right> \\longrightarrow \\frac{(\\left|0\\right>+e^{2\\pi i[0.x_{n}]}\\left|1\\right>)\\otimes (\\left|0\\right>+e^{2\\pi i[0.x_{n-1}x_{n}]}\\left|1\\right>)\\otimes \\dots \\otimes (\\left|0\\right>+e^{2\\pi i[0.x_{1}x_{2}\\dots x_{n}]}\\left|1\\right>)}{2^{n/2}}.$$\n",
    "For example, the QFT on three qubits can be written as \n",
    "\n",
    "$$\\mathrm{QFT}\\left|x_{1}x_{2}x_{3}\\right> = \\frac{1}{2^{3/2}}\\left(\\left|0\\right>+e^{2\\pi i[0.x_{3}]}\\left|1\\right>\\right) \\otimes \\left(\\left|0\\right>+e^{2\\pi i[0.x_{2}x_{3}]}\\left|1\\right>\\right) \\otimes \\left(\\left|0\\right>+e^{2\\pi i[0.x_{1}x_{2}x_{3}]}\\left|1\\right>\\right).$$\n",
    "\n",
    "Thus, for the simple input state $\\left|0,0,0\\right>$ with $x_{i}=0$, it is easy to see that the QFT produces a uniform superposition of all computational basis vectors (since only the Hadamard gates act non-trivially in this case).  Explicitly:\n",
    "$$\n",
    "\\begin{split}\n",
    "\\mathrm{QFT}\\left|0,0,0\\right> & = \\frac{1}{\\sqrt{2^{3}}}(\\left|0\\right>+\\left|1\\right>) \\otimes (\\left|0\\right>+\\left|1\\right>) \\otimes (\\left|0\\right>+\\left|1\\right>) \\\\\n",
    " & = \\frac{1}{\\sqrt{2^{3}}} \\bigotimes_{i} \\left|+\\right>_{i}\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "## Inverse QFT  \n",
    "Below we will also implement the inverse QFT algorithm (denoted by $\\mathrm{QFT}^{\\dagger}$, or sometimes $\\mathrm{QFT}^{-1}$), which fulfills $\\mathrm{QFT}\\cdot\\mathrm{QFT}^{\\dagger}=\\mathbb{1}$, where $\\mathbb{1}$ is the identity. For example, with the inverse QFT we can invert the above three qubit QFT as \n",
    "\n",
    "$$\\mathrm{QFT}^\\dagger\\mathrm{QFT}\\left|x_{1}x_{2}x_{3}\\right> = \\mathrm{QFT}^{\\dagger}(\\left|0\\right>+e^{2\\pi i[0.x_{3}]}\\left|1\\right>) \\otimes (\\left|0\\right>+e^{2\\pi i[0.x_{2}x_{3}]}\\left|1\\right>) \\otimes (\\left|0\\right>+e^{2\\pi i[0.x_{1}x_{2}x_{3}]}\\left|1\\right>)/2^{3/2}=\\left|x_{1}x_{2}x_{3}\\right>.$$\n",
    "\n",
    "__Example for inverse QFT:__ For further illustration, we will run a concrete example of this kind below. \n",
    "Specifically, consider the following example with $x_{1}=0$, $x_{2}=1$, and $x_{3}=0$ encoding the number 2 in binary representation. \n",
    "Accordingly, we prepare the initial state (up to normalization)\n",
    "\n",
    "$$\\left|\\Psi_\\mathrm{in}\\right>=(\\left|0\\right>+e^{2\\pi i[0.0]}\\left|1\\right>) \\otimes (\\left|0\\right>+e^{2\\pi i[0.10]}\\left|1\\right>) \\otimes (\\left|0\\right>+e^{2\\pi i[0.010]}\\left|1\\right>),$$\n",
    "which is equivalent to \n",
    "$$\\left|\\Psi_\\mathrm{in}\\right>=(\\left|0\\right>+\\left|1\\right>) \\otimes (\\left|0\\right>+e^{2\\pi i\\frac{1}{2}}\\left|1\\right>) \\otimes (\\left|0\\right>+e^{2\\pi i\\frac{1}{4}}\\left|1\\right>).$$\n",
    "\n",
    "This state can be prepared using the single-qubits gates $H$ and $R_{z}$ as follows: \n",
    "\n",
    "$$\\left|\\Psi_\\mathrm{in}\\right>=H\\left|0\\right> \\otimes R_{z}(\\pi)H\\left|0\\right> \\otimes R_{z}(\\pi/2)H\\left|0\\right>.$$\n",
    "\n",
    "Based on the analysis above we then expect $\\mathrm{QFT}^{\\dagger} \\left|\\Psi_\\mathrm{in}\\right> = \\left|0,1,0\\right>$.\n",
    "We can generalize the above example to multiple qubits with the following state preparation code:\n",
    "```python\n",
    "circ = Circuit()\n",
    "circ.h(range(num_qubits))\n",
    "for ii in range(num_qubits - 1):\n",
    "    circ.rz(ii+1, math.pi/(2**ii))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation of QFT  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The QFT circuit can be implemented using Hadamard gates, controlled phase gates, and SWAP gates. The Hadamard gate $H$, the phase gate ${\\displaystyle R_{m}}$, and the SWAP gate are given by\n",
    "$$H = \\frac{1}{\\sqrt{2}}\n",
    "\\begin{pmatrix} \n",
    "1 & 1\\\\\n",
    "1 & -1\\\\\n",
    "\\end{pmatrix} \\qquad \\qquad\n",
    "R_{m} = \n",
    "\\begin{pmatrix} \n",
    "1 & 0\\\\\n",
    "0 & e^{\\frac{2\\pi i}{2^{m}}}\\\\\n",
    "\\end{pmatrix} \\qquad \\qquad\n",
    "\\mathrm{SWAP} = \n",
    "\\begin{pmatrix} \n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 1\\\\\n",
    "\\end{pmatrix}.$$"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Braket Implementation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# General imports\n",
    "import boto3\n",
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "# magic word for producing visualizations in notebook\n",
    "%matplotlib inline\n",
    "import string\n",
    "import time\n",
    "from datetime import datetime\n",
    "# import logging\n",
    "import logging\n",
    "\n",
    "# AWS imports: Import Braket SDK modules\n",
    "from braket.circuits import Circuit, Gate, Instruction, circuit, Observable\n",
    "from braket.aws import AwsDevice, AwsQuantumTask\n",
    "from braket.devices import LocalSimulator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# S3 storage\n",
    "my_bucket = f\"amazon-braket-xxx\" #\"amazon-braket-xxx\" # the name of the bucket\n",
    "my_prefix = \"qft-qpe-output\" # the name of the folder in the bucket\n",
    "s3_folder = (my_bucket, my_prefix)\n",
    "\n",
    "# set up the device to be the managed simulator\n",
    "device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/sv1\")\n",
    "# device = LocalSimulator()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "## QFT function\n",
    "def qft(qubits):    \n",
    "    \"\"\"\n",
    "    Construct a circuit object corresponding to the Quantum Fourier Transform (QFT)\n",
    "    algorithm, applied to the argument qubits.  Does not use recursion to generate the QFT.\n",
    "    \n",
    "    Args:\n",
    "        qubits (int): The list of qubits on which to apply the QFT\n",
    "    \"\"\"\n",
    "    qftcirc = Circuit()\n",
    "    \n",
    "    # get number of qubits\n",
    "    num_qubits = len(qubits)\n",
    "    \n",
    "    for k in range(num_qubits):\n",
    "        # First add a Hadamard gate\n",
    "        qftcirc.h(qubits[k])\n",
    "    \n",
    "        # Then apply the controlled rotations, with weights (angles) defined by the distance to the control qubit.\n",
    "        # Start on the qubit after qubit k, and iterate until the end.  When num_qubits==1, this loop does not run.\n",
    "        for j in range(1,num_qubits - k):\n",
    "            angle = 2*math.pi/(2**(j+1))\n",
    "            qftcirc.cphaseshift(qubits[k+j],qubits[k], angle)\n",
    "            \n",
    "    # Then add SWAP gates to reverse the order of the qubits:\n",
    "    for i in range(math.floor(num_qubits/2)):\n",
    "        qftcirc.swap(qubits[i], qubits[-i-1])\n",
    "        \n",
    "    return qftcirc\n",
    "\n",
    "## Inverse QFT function\n",
    "def inverse_qft(qubits):\n",
    "    \"\"\"\n",
    "    Construct a circuit object corresponding to the inverse Quantum Fourier Transform (QFT)\n",
    "    algorithm, applied to the argument qubits.  Does not use recursion to generate the circuit.\n",
    "    \n",
    "    Args:\n",
    "        qubits (int): The list of qubits on which to apply the inverse QFT\n",
    "    \"\"\"\n",
    "    # instantiate circuit object\n",
    "    qftcirc = Circuit()\n",
    "    \n",
    "    # get number of qubits\n",
    "    num_qubits = len(qubits)\n",
    "    \n",
    "    # First add SWAP gates to reverse the order of the qubits:\n",
    "    for i in range(math.floor(num_qubits/2)):\n",
    "        qftcirc.swap(qubits[i], qubits[-i-1])\n",
    "        \n",
    "    # Start on the last qubit and work to the first.\n",
    "    for k in reversed(range(num_qubits)):\n",
    "    \n",
    "        # Apply the controlled rotations, with weights (angles) defined by the distance to the control qubit.\n",
    "        # These angles are the negative of the angle used in the QFT.\n",
    "        # Start on the last qubit and iterate until the qubit after k.  \n",
    "        # When num_qubits==1, this loop does not run.\n",
    "        for j in reversed(range(1, num_qubits - k)):\n",
    "            angle = -2*math.pi/(2**(j+1))\n",
    "            qftcirc.cphaseshift(qubits[k+j],qubits[k], angle)\n",
    "            \n",
    "        # Then add a Hadamard gate\n",
    "        qftcirc.h(qubits[k])\n",
    "    \n",
    "    return qftcirc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examples of QFT circuits  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "QFT CIRCUIT:\n",
      "T  : |0|     1     |2| 3  |\n",
      "                           \n",
      "q0 : -H-PHASE(1.57)---SWAP-\n",
      "        |             |    \n",
      "q1 : ---C-----------H-SWAP-\n",
      "\n",
      "T  : |0|     1     |2| 3  |\n",
      "\n",
      "INVERSE-QFT CIRCUIT:\n",
      "T  : | 0  |1|     2      |3|\n",
      "                            \n",
      "q0 : -SWAP---PHASE(-1.57)-H-\n",
      "      |      |              \n",
      "q1 : -SWAP-H-C--------------\n",
      "\n",
      "T  : | 0  |1|     2      |3|\n"
     ]
    }
   ],
   "source": [
    "# show inverse QFT example circuit\n",
    "num_qubits = 2\n",
    "qubits=range(num_qubits)\n",
    "my_qft_circ = qft(qubits)\n",
    "print('QFT CIRCUIT:')\n",
    "print(my_qft_circ)\n",
    "\n",
    "# show inverse QFT example circuit\n",
    "print('')\n",
    "print('INVERSE-QFT CIRCUIT:')\n",
    "my_iqft_circ = inverse_qft(qubits)\n",
    "print(my_iqft_circ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantum Phase Estimation  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Background**\n",
    "\n",
    "__Quantum Phase Estimation Algorithm__: \n",
    "The QPE algorithm takes a unitary $U$ as input. For the sake of simplicity (we will generalize the discussion below), suppose that the algorithm also takes as input an eigenstate $|\\psi \\rangle$ fulfilling \n",
    "\n",
    "$$U|\\psi \\rangle = \\lambda |\\psi \\rangle,$$\n",
    "\n",
    "with $\\lambda = \\exp(2\\pi i\\varphi)$. \n",
    "\n",
    "QPE uses two registers of qubits: we will refer to the first register as *precision* qubits (as the number of qubits $n$ in the first register sets the achievable precision of our results) and the second register as *query* qubits (as the second register hosts the eigenstate $|\\psi \\rangle$). \n",
    "Suppose we have prepared this second register in $|\\psi \\rangle$.  We then prepare a uniform superposition of all basis vectors in the first register using a series of Hadamard gates. \n",
    "\n",
    "Next, we apply a series of controlled-unitaries $C-U^{2^{k}}$ for different powers of $k=0,1,\\dots, n-1$ (as illustrated in the circuit diagram below). \n",
    "For example, for $k=1$ we get\n",
    "\\begin{equation} \n",
    "\\begin{split}\n",
    "(|0 \\rangle + |1 \\rangle) |\\psi \\rangle  & \\rightarrow |0 \\rangle |\\psi \\rangle + |1 \\rangle U|\\psi \\rangle \\\\\n",
    "& = (|0 \\rangle + e^{2\\pi i \\varphi}|1 \\rangle) |\\psi \\rangle.\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "Note that the second register remains unaffected as it stays in the eigenstate $|\\psi \\rangle$. \n",
    "However, we managed to transfer information about the phase of the eigenvalue of $U$ (i.e., $\\varphi$) into the first *precision* register by encoding it as a relative phase in the state of the qubits in the first register. \n",
    "\n",
    "Similarly, for $k=2$ we obtain\n",
    "\\begin{equation} \n",
    "\\begin{split}\n",
    "(|0 \\rangle + |1 \\rangle) |\\psi \\rangle  & \\rightarrow |0 \\rangle |\\psi \\rangle + |1 \\rangle U^{2}|\\psi \\rangle \\\\\n",
    "& = (|0 \\rangle + e^{2\\pi i 2\\varphi}|1 \\rangle) |\\psi \\rangle,\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "where this time we wrote $2\\varphi$ into the precision register. The process is similar for all $k>2$.\n",
    "\n",
    "Introducing the following notation for binary fractions\n",
    "$$[0. \\varphi_{l}\\varphi_{l+1}\\dots \\varphi_{m}] = \\frac{\\varphi_{l}}{2^{1}} + \\frac{\\varphi_{l+1}}{2^{2}} + \\frac{\\varphi_{m}}{2^{m-l+1}},$$ \n",
    "\n",
    "one can easily show that the application of a controlled unitary $C-U^{2^{k}}$ leads to the following transformation\n",
    "\n",
    "\\begin{equation} \n",
    "\\begin{split}\n",
    "(|0 \\rangle + |1 \\rangle) |\\psi \\rangle  & \\rightarrow |0 \\rangle |\\psi \\rangle + |1 \\rangle U^{2^{k}}|\\psi \\rangle \\\\\n",
    "& = (|0 \\rangle + e^{2\\pi i 2^{k}\\varphi}|1 \\rangle) |\\psi \\rangle \\\\\n",
    "& = (|0 \\rangle + e^{2\\pi i [0.\\varphi_{k+1}\\dots \\varphi_{n}]}|1 \\rangle) |\\psi \\rangle,\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "where the first $k$ bits of precision in the binary expansion (i.e., those bits to the left of the decimal) can be dropped, since $e^{2\\pi i \\theta} = 1$ for any whole number $\\theta$.\n",
    "\n",
    "The QPE algorithm implements a series of these transformations for $k=0, 1, \\dots, n-1$, using $n$ qubits in the precision register. \n",
    "In its entirety, this sequence of controlled unitaries leads to the transformation\n",
    "\n",
    "$$ |0, \\dots, 0 \\rangle \\otimes |\\psi \\rangle \\longrightarrow \n",
    "(|0 \\rangle + e^{2\\pi i [0.\\varphi_{n}]}|1 \\rangle) \n",
    "\\otimes (|0 \\rangle + e^{2\\pi i [0.\\varphi_{n-1}\\varphi_{n}]}|1 \\rangle)\n",
    "\\otimes \\dots\n",
    "\\otimes (|0 \\rangle + e^{2\\pi i [0.\\varphi_{1}\\dots\\varphi_{n}]}|1 \\rangle) \n",
    "\\otimes |\\psi \\rangle.\n",
    "$$\n",
    "\n",
    "By inspection, one can see that the state of the register qubits above corresponds to a quantum Fourier transform of the state $|\\varphi_1,\\dots,\\varphi_n\\rangle$. Thus, the final step of the QPE algorithm is to run the *inverse* Quantum Fourier Transform (QFT) algorithm on the precision register to extract the phase information from this state. The resulting state is\n",
    "$$|\\varphi_{1}, \\varphi_{2}, \\dots, \\varphi_{n}  \\rangle \\otimes |\\psi\\rangle.$$\n",
    "\n",
    "Measuring the precision qubits in the computational basis then gives the classical bitstring $\\varphi_{1}, \\varphi_{2}, \\dots, \\varphi_{n}$, from which we can readily infer the phase estimate $\\tilde{\\varphi} = 0.\\varphi_{1} \\dots \\varphi_{n}$ with the corresponding eigenvalue $\\tilde{\\lambda} = \\exp(2\\pi i \\tilde{\\varphi})$.\n",
    " \n",
    "__Simple example for illustration__: For concreteness, let us consider a simple example with the unitary given by the Pauli $X$ gate, $U=X$, for which $|\\Psi \\rangle = |+\\rangle = (|0 \\rangle + |1 \\rangle)/\\sqrt{2}$ is an eigenstate with eigenvalue $\\lambda = 1$, i.e., $\\varphi=0$. \n",
    "This state can be prepared simply with a Hadamard gate as $|\\Psi \\rangle = H|0 \\rangle$. \n",
    "We take a precision register consisting of just two qubits ($n=2$). \n",
    "\n",
    "Thus, after the first layer of Hadamard gates, the quantum state is\n",
    "$$|0,0,0 \\rangle \\rightarrow |+,+,+\\rangle.$$\n",
    "\n",
    "Next, the applications of the controlled-$U$ gates (equal to $C-X$ operations, or CNOT gates in this example) leave this state untouched, since $|+\\rangle$ is an eigenstate of $X$ with eigenvalue $+1$. \n",
    "Finally, applying the inverse QFT leads to \n",
    "\n",
    "$$\\mathrm{QFT}^{\\dagger}|+++\\rangle=\\mathrm{QFT}^\\dagger\\frac{|00\\rangle + |01\\rangle + |10\\rangle + |11\\rangle}{4}\\otimes |+\\rangle = |00\\rangle \\otimes |+\\rangle,$$\n",
    "\n",
    "from which we deduce $\\varphi = [0.00]=0$ and therefore $\\lambda=1$, as expected. \n",
    "Here, in the last step we have used $|00\\rangle + |01\\rangle + |10\\rangle + |11\\rangle = (|0\\rangle + e^{2\\pi i[0.0]}|1\\rangle)(|0\\rangle + e^{2\\pi i[0.00]}|1\\rangle)$, which makes the effect of the inverse QFT more apparent.  \n",
    "\n",
    "__Initial state of query register__: So far, we have assumed that the query register is prepared in an eigenstate $|\\Psi\\rangle$ of $U$. What happens if this is not the case? Let's reconsider the simple example above.\n",
    "\n",
    "Suppose now that the query register is instead prepared in the state $|\\Psi\\rangle = |1\\rangle$. \n",
    "We can always express this state in the eigenbasis of $U$, i.e., $|1\\rangle = \\frac{1}{\\sqrt{2}}(|+\\rangle - |-\\rangle)$. \n",
    "By linearity, application of the QPE algorithm then gives (up to normalization)\n",
    "\n",
    "\\begin{equation} \n",
    "\\begin{split}\n",
    "\\mathrm{QPE}(|0,0,\\dots\\rangle \\otimes |1\\rangle) & = \\mathrm{QPE}(|0,0,\\dots\\rangle \\otimes |+\\rangle)\n",
    "- \\mathrm{QPE}(|0,0,\\dots\\rangle \\otimes |-\\rangle) \\\\\n",
    "& =  |\\varphi_{+}\\rangle \\otimes |+\\rangle - |\\varphi_{-}\\rangle \\otimes |-\\rangle. \\\\\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "When we measure the precision qubits in this state, 50% of the time we will observe the eigenphase $\\varphi_{+}$ and 50% of the time we will measure $\\varphi_{-}$. We illustrate this example numerically below.\n",
    "\n",
    "This example motivates the general case: we can pass a state that is not an eigenstate of $U$ to the QPE algorithm, but we may need to repeat our measurements several times in order to obtain an estimate of the desired phase."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## QPE Circuit  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The QPE circuit can be implemented using Hadamard gates, controlled-$U$ unitaries, and the inverse QFT (denoted as $\\mathrm{QFT}^{-1}$). \n",
    "Following the discussion above, the circuit that implements the QPE algorithm reads as below, where m is the size of lower query register and n is the size of upper precision register."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## QPE Example "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us determine the eigenstates of Pauli $X = \\begin{pmatrix} \n",
    "0 & 1\\\\\n",
    "1 & 0\\\\\n",
    "\\end{pmatrix}$ operator using QPE with the two-qubit query register. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Controlled Unitary circuit\n",
    "def cU(cInd, tInd):\n",
    "    return Circuit().cnot(cInd,tInd)\n",
    "\n",
    "\n",
    "def str2circ(s, indQ0):\n",
    "    circ = Circuit()\n",
    "    for ind in range(len(s)):\n",
    "        if s[ind]=='1':\n",
    "            circ.x(ind+indQ0)\n",
    "    return circ\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T  : |0|1|2|3| 4  |5|     6      |7|\n",
      "                                    \n",
      "q0 : -H---C-C-SWAP---PHASE(-1.57)-H-\n",
      "          | | |      |              \n",
      "q1 : -H-C-|-|-SWAP-H-C--------------\n",
      "        | | |                       \n",
      "q2 : -H-X-X-X-H---------------------\n",
      "\n",
      "T  : |0|1|2|3| 4  |5|     6      |7|\n",
      "Counter({'000': 1000})\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# QPE circuit for |+> eigenstate of X\n",
    "circ_QPE = Circuit().h(0).h(1).h(2)\n",
    "circ_QPE = circ_QPE.add_circuit(cU(1,2))\n",
    "circ_QPE = circ_QPE.add_circuit(cU(0,2))\n",
    "circ_QPE = circ_QPE.add_circuit(cU(0,2))\n",
    "circ_QPE = circ_QPE.add_circuit(inverse_qft([0,1]))\n",
    "circ_QPE = circ_QPE.add_circuit(Circuit().h(2))\n",
    "\n",
    "print (circ_QPE)\n",
    "\n",
    "task = device.run(circ_QPE, s3_folder, shots=1000)\n",
    "result = task.result()\n",
    "\n",
    "## Get measurement counts\n",
    "counts = result.measurement_counts\n",
    "\n",
    "# print counts\n",
    "print(counts)\n",
    "\n",
    "# plot using Counter\n",
    "plt.bar(counts.keys(), counts.values());\n",
    "plt.xlabel('bitstrings');\n",
    "plt.ylabel('counts');\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "conda_braket",
   "language": "python",
   "name": "conda_braket"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
